Condition for Straight Lines in Plane to be Perpendicular/Examples/Arbitrary Example 1
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Examples of Use of Condition for Straight Lines in Plane to be Perpendicular
Let $\LL_1$ be the straight line whose equation in general form is given as:
- $3 x - 4 y = 7$
Let $\LL_2$ be the straight line perpendicular to $\LL_1$ which passes through the point $\tuple {1, 2}$.
The equation for $\LL_2$ is:
- $4 x + 3 y = 10$
Proof
From Corollary to Condition for Straight Lines in Plane to be Perpendicular, $\LL_2$ has an equation of the form:
- $(1): \quad 4 x + 3 y = C$
We have that $\tuple {1, 2}$ is on $\LL_2$.
Hence substituting $x = 1$ and $y = 2$ into $(1)$:
\(\ds C\) | \(=\) | \(\ds 4 \paren 1 + 3 \paren 2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 10\) |
Hence the result.
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {III}$. Analytical Geometry: The Straight Line: The angle between two lines: Example $\text{(ii)}$